Note on Equalizer:
The damage done scales inversely with health. Approximately 113.7 − 0.405x, where x is the amount of health the player currently has, with a minimum of 33 when the player is at or above 200 health, and a maximum of 113 (before random damage and Critical hits). It should also be noted the Equalizer is the weakest melee weapon when Soldier has max health, and the strongest next to Spy's Backstab when Soldier is low.

For the Range of the weapons, I couldn't find weapon-specific range, the same Wiki states:

The Eyelander's melee range is approximately 37% more than the Bottle and other melee weapons. The same is true for the Scotsman's skullcutter.